After being rushed to Baylor University Medical Center, Jean was pronounced dead, according to The Dallas Morning News. He died shortly after.
The shooting happened just before 10pm at South Side Flats, an upscale apartment complex in downtown Dallas.
Neighbours said they can access their building with a regular key or by using a keypad code. She said the officer hadn't yet been questioned.
"This is a very unique situation", Hall explained.
"A blood sample was drawn to test for drugs and alcohol, we are in the process of obtaining a warrant, and we have also invited the Texas Rangers to conduct an independent investigation", she said, referring to the state law enforcement agency.
"We're going to try to get the special treatment of police officers who kill someone ended".
"If this was not an officer who pulled the trigger, they would be in a jail cell tonight", Dallas Muslim community leader Omar Suleiman said during the vigil.
Trump's actions 'detrimental' to country's health, says anonymous official
FILE - White House press secretary Sarah Sanders speaks during a press briefing at the White House, May 7, 2018. In an official written statement, the White House also attacked the opinion column and criticized its author.
Chief U. Renee Hall said at a news conference Friday that "there are more questions than we have answers" in the Thursday night killing of 26-year-old Botham Jean, but that with the information investigators have now, they're seeking a manslaughter charge against the officer. He always wanted to lead in chapel in whatever way he could.
The Christian Chronicle reports that he is being remembered for his lovely singing voice - he often led songs during services - and the depth of his faith.
Hall said she had spoken with Jean's sister and offered the family condolences.
Family members have taken to Facebook to grieve the loss of Jean.
"How can this nasty world take you away from me.this is the worst day of my life thus far.uncle loves you so much", he wrote. "Lord, keep me sane".
On his LinkedIn profile, Jean described himself as an "aspiring young professional" who worked as a risk assurance associate for PricewaterhouseCoopers in Dallas.
"This is a awful tragedy", the company said in a statement". She was visiting a daughter in Florida when she learned her son had been killed. "It just feels like a nightmare", Allison told NBC News. "I wish I would wake up and find that it wasn't true".
It was unclear if the officer knew Jean, 26, who lived in the same apartment complex as each other.